The coaster brake is all in the hub. There is the arm that bolts to the chain stay, by the rear wheel. The brake itself is inside of the left side of the hub. You can run a coaster brake on your 73 schwinn, but you need to make sure that the cruiser's wheel will fit properly in the collegiate. I'm not up on schwinns, but that'll be your biggest obstacle, as well as making sure that your coasterbrake hub is the right over-locknut dimension for the other frame, and vice-versa.
Many ppl might advise against this swap, fyi.
So you plan to put a coaster brake hub in the 5 speed bike, that will not be a problem.
here is what you do :
get a coaster brake hub, whose axle is long enough to span the dropouts and accept the Nuts and washers that go on the outside.
and then have it laced up in the same size rim, as you have on the 5 speed,
or if its in rather good shape, de-tension the spokes ,
( take the cluster of sprockets off the hub first or, it hub and cluster, will be garbage,
you need the rim on the wheel to get the leverage to remove the freewheel )
and then, you can re use the rim in the new back wheel.
you did not state whether the wheel sizes on the 2 bikes are the same dimensions,
So I assume they are not. hence the rebuild the wheel reccomendation ..
As 5 speed derailleur frames are 120 wide in the rear , you also have the option of a 3 speed internal gear hub
with a coaster brake . that would make it into a pretty decent practical bike.
and cogs on 3 speeds come in a good range of sizes 14 to 20 teeth.
which is an advantage in setting up what the ratios of the drive sprockets are to be ...
But really Its still geared as there is a chain and 2 sprockets of differing sizes
now if you take up Unicycling, then you can really get rid of the gears.